Including averages logic into IF formulas

The Data: I have 3 columns of data that may or may not have a numerical value greater than 0.

The Problem: I want to take an average of those three columns but not include the zeros in the average.

An Example:
A = 2
B = 4
C = 6
Avg = 4

BUT if a value in one of the columns is zero I don't want to include it in the average:
A = 0
B = 4
C = 6
Avg = 5 (rather than 3.33)